# Computation of moments in quadratic discontinuous anisotropic plane elasticity fast multipole formulation

## Palavras-chave:

anisotropic plane elasticity, fast multipole method, boundary element method, quadratic discontinuous elements## Resumo

The fast multipole formulation is used in order to solve large scale problems in general boundary el-

ement formulation. In this work we will present the computation of moments in the anisotropic plane elasticity

fast multipole formulation with quadratic discontinuous elements. Fundamental solutions of plane elasticity are

represented by complex functions from the classical 2D elasticity theory. The Multipole Expansion for kernels U

(displacement field) and T (traction field) will be computed using series. The convergence of the series expansion

to the fundamental solutions is analyzed considering different numbers of series terms and different distance from

source point to field point. Moments are computed to evaluate integrals of influence matrices where elements are

far away from the source point, whereas the conventional approach will be applied to evaluate the integrals on the

remaining elements that are closer to the source point. All fast multipole operations are demonstrated in this work

and compared to the standard boundary element formulation.